Ratio of Uranium in a Specific Sample
Essay by ks11 • April 22, 2012 • Coursework • 566 Words (3 Pages) • 1,801 Views
Assignment 3
Question 1.
Ratio of molecules in initial concentration
235U/238U in a particular rock sample was 2.0%
235U half-life = 7.04 x 108 238U half-life = 4.5 x 109
4.5 billion years = 4.5 x 109
number of half-lives occurred = (total time elapsed ÷ length of half-life)
(4.5 x 10^9)/( 7.04 x 10^8) = 6.42 half lives (4.5 x 10^9)/(4.5 x 10^9) = 1 half life
(starting amount) x (1/2)number of half-lives
After 6.42 half-lives the fraction of U235 = 2 / 26.42 = .0234
After 1 half-life the fraction of U238 = 100 / 21 = 50
0.0234:50 = .046% U235
Question 2.
A single U-235 atom releases approximately 200 MeV (million electron volt) http://science.howstuffworks.com/nuclear-power1.htm
235g of U-235 contains Avogadro's number of atoms and 1 kg contains-
1000g X (6.02 x 1023 2 2 235g =2.563x 1024 Atoms
Energy released = # of atoms X energy released per fission
2.563 x 1024 X 200 MeV = 5.126 X 1026 MeV
1 MeV = 106 x 1.6 x 10-19 = 1.6 x 10-13 J http://www.a-levelphysicstutor.com/nucphys-fission.php
The energy released is 1.6 x 10-13 J x 5.126 X 1026 MeV = 8.2X 1013 J = 8.2X 1010 KJ
1 CH4 = (802 Kj )/(mol CH4) X (mol CH4)/16g = 50.12 Kj / CH4
1 kg = 1000g = 50.1 Kj x 1000g = 5.01 x 104 Kj / Kg
Ratio ( 8.20X 10^10 Kj)/(5.01 x 10^4 Kj ) = 1.6 X 106 U-235 : 1 CH4
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